Ever since I had upgraded to 10.6.7, or about the same time, my iPhone was no longer backing up.

It was giving me 2 errors: 'Couldn't retrieve profile from Sync Services -- unplug and replug iPhone' and 'Couldn't backup iPhone.' Having restarted, and unplugged/replugged the iPhone, it still wouldn't back up, or even update to iOS 4.3.1. The situation was very vexing.

The issue was available storage space on the iPhone. I had over 700 photos and movies on my 16GB iPhone, which clogged everything up. The solution, of course, was to delete those photos and videos. Having done that, the iPhone finally synched, backed up and updated to 4.3.1.

It may be slightly obvious, but it's good to know that too little disk space on the iPhone can clog up backups.

[crarko adds: Is there documentation about how much scratch space needs to be left on iOS devices for things like updates? A pointer would be handy if somebody could provide it.]

I was receiving the same error this weekend. However in my case something relating to the iTunes application itself was damaged. I trashed all iTunes packages from /Library/Receipts, then re-downloaded iTunes from the Apple website. Backups started working just fine after that. Just thought I'd share this in case someone has the same issue.

I was experiencing the same thing, but it was ever since installing XCode 4, and it had nothing to do with free space (my phone is 16BG iPhone 4 with 5.4 GB free). I had to follow an apple KB article that removed some stuff in /System/Library and reinstalled iTunes. I'll post the article link later once I'm back at my personal computer again.
Edit:
I looked again, and I was actually receiving a similar, but different error message. Perhaps I'll have to submit a Hint on it.

On my original 8GB iPhone through iOS 3.0.x, I was able to keep as little as 100MB free space, and, believe me, I was gaming every KB I could get on that phone; each time I bought new app, even though it would install inside that 100MB, the next time I went to sync it would refuse to sync my photos until I either reduced photos or music to accommodate down to 1MB of the discrepancy.

An Apple Genius told me they'd gotten a lot of complaints about the same thing, and that they were instructed to tell people that it was necessary to restrict the space further than prior iterations needs for memory swap and cache files to allow for video capture; that more people were upset that they could not capture video when they wanted and they could not easily free up space on the fly by deleting music or other easily replaced items.

So, sorry, I do not have a tech reference on minimum free space, only my seat of the pants experience in what that space demand is (again, roughly 5% of actual storage capacity).